Instrumental Variables Estimation With Some Invalid Instruments and its Application to Mendelian Randomization

Instrumental variables have been widely used for estimating the causal effect between exposure and outcome. Conventional estimation methods require complete knowledge about all the instruments’ validity; a valid instrument must not have a direct effect on the outcome and not be related to unmeasured confounders. Often, this is impractical as highlighted by Mendelian randomization studies where genetic markers are used as instruments and complete knowledge about instruments’ validity is equivalent to complete knowledge about the involved genes’ functions. In this article, we propose a method for estimation of causal effects when this complete knowledge is absent. It is shown that causal effects are identified and can be estimated as long as less than 50% of instruments are invalid, without knowing which of the instruments are invalid. We also introduce conditions for identification when the 50% threshold is violated. A fast penalized ℓ1 estimation method, called sisVIVE, is introduced for estimating the causal effect without knowing which instruments are valid, with theoretical guarantees on its performance. The proposed method is demonstrated on simulated data and a real Mendelian randomization study concerning the effect of body mass index(BMI) on health-related quality of life (HRQL) index. An R package sisVIVE is available on CRAN. Supplementary materials for this article are available online.

• Publication year

  2014

• Venue

  Journal of the American Statistical Association

• Publication date

  2014-01-22

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1080/01621459.2014.994705arXiv 1401.5755
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Identification and Inference With Many Invalid Instruments

  2015cited by this paper
• Haplotypes in the CRP Gene Associated with Increased BMI and Levels of CRP in Subjects with Type 2 Diabetes or Obesity from SouthwesternMexico América Martı́nez -

  2014cited by this paper
• Can we make smart choices between OLS and contaminated IV methods?

  2014cited by this paper
• Compressed Sensing and Affine Rank Minimization Under Restricted Isometry

  2013cited by this paper
• Using Secondary Outcomes to Sharpen Inference in Randomized Experiments With Noncompliance

  2013cited by this paper
• Pleiotropy in complex traits: challenges and strategies

  2013cited by this paper
• Multigene interactions and the prediction of depression in the Wisconsin Longitudinal Study

  2012cited by this paper
• Haplotypes in the CRP Gene Associated with Increased BMI and Levels of CRP in Subjects with Type 2 Diabetes or Obesity from Southwestern Mexico

  2012cited by this paper
• Credible Mendelian randomization studies: approaches for evaluating the instrumental variable assumptions.

  2012cited by this paper
• The Lasso Problem and Uniqueness

  2012cited by this paper
• The medical care costs of obesity: an instrumental variables approach.

  2012influential reference
• Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain

  2012cited by this paper
• A Review of Econometric Analysis of Cross Section and Panel Data (2nd ed.)

  2011cited by this paper
• High-dimensional instrumental variables regression and confidence sets

  2011cited by this paper
• Statistics for High-Dimensional Data: Methods, Theory and Applications

  2011cited by this paper
• 双対平坦空間におけるLeast Angle Regressionと情報量規準

  2009cited by this paper
• Two British women studies replicated the association between the Val66Met polymorphism in the brain-derived neurotrophic factor (BDNF) and BMI

  2009cited by this paper
• Genome-wide association yields new sequence variants at seven loci that associate with measures of obesity

  2009cited by this paper
• Association Study and Mutation Analysis of Adiponectin Shows Association of Variants in APM1 with Complex Obesity in Women

  2009cited by this paper
• FTO gene SNPs associated with extreme obesity in cases, controls and extremely discordant sister pairs

  2008cited by this paper
• A Simple Proof of the Restricted Isometry Property for Random Matrices

  2008influential reference
• ‘Mendelian randomization’ equals instrumental variable analysis with genetic instruments

  2008cited by this paper
• War and Wages

  2008cited by this paper
• Celebrating the 25 th Anniversary of Statistics in Medicine Mendelian randomization : Using genes as instruments for making causal inferences in epidemiology

  2008cited by this paper
• The relationship between body mass index and health-related quality of life: comparing the EQ-5D, EuroQol VAS and SF-6D

  2007cited by this paper
• Variation in FTO contributes to childhood obesity and severe adult obesity

  2007cited by this paper
• Adiponectin SNP276 is associated with obesity, the metabolic syndrome, and diabetes in the elderly.

  2007cited by this paper
• War and Wages : The Strength of Instrumental Variables and Their Sensitivity to Unobserved Biases

  2007cited by this paper
• Sensitivity Analysis for Instrumental Variables Regression With Overidentifying Restrictions

  2007influential reference
• ACDC/adiponectin polymorphisms are associated with severe childhood and adult obesity.

  2006cited by this paper
• Avoiding Invalid Instruments and Coping with Weak Instruments

  2006cited by this paper
• Instruments for Causal Inference: An Epidemiologist's Dream?

  2006cited by this paper
• For most large underdetermined systems of linear equations the minimal 𝓁1‐norm solution is also the sparsest solution

  2006cited by this paper
• The Val66Met polymorphism of the brain-derived neurotrophic-factor gene is associated with geriatric depression.

  2006cited by this paper
• Just relax: convex programming methods for identifying sparse signals in noise

  2006cited by this paper
• Prefrontal cognition in schizophrenia and bipolar illness in relation to Val66Met polymorphism of the brain‐derived neurotrophic factor gene

  2006cited by this paper
• [Mendelian randomization].

  2005cited by this paper
• C-reactive protein and its role in metabolic syndrome: mendelian randomisation study.

  2005cited by this paper
• Survey Response in the Long Run: The Wisconsin Longitudinal Study

  2005cited by this paper
• Decoding by linear programming

  2005cited by this paper
• Mendelian randomization: prospects, potentials, and limitations.

  2004cited by this paper
• Commentary: the concept of 'Mendelian Randomization'.

  2004cited by this paper
• Apolipoprotein E isoforms, serum cholesterol, and cancer. 1986.

  2004cited by this paper
• Commentary: Mendelian randomization and gene-environment interaction.

  2004cited by this paper
• Solutions Manual and Supplementary Materials for Econometric Analysis of Cross Section and Panel Data

  2003influential reference
• Allele-specific differential expression of a common adiponectin gene polymorphism related to obesity

  2003cited by this paper
• 'Mendelian randomization': can genetic epidemiology contribute to understanding environmental determinants of disease?

  2003cited by this paper
• Mutations in the adiponectin gene in lean and obese subjects from the Swedish obese subjects cohort.

  2003cited by this paper
• The Elements of Statistical Learning

  2003cited by this paper
• Mendelian randomisation: a new spin or real progress?

  2003cited by this paper
• Econometric Analysis of Cross Section and Panel Data

  2002cited by this paper
• A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments

  2002cited by this paper
• ALTERNATIVE METHODS FOR EVALUATING THE IMPACT OF INTERVENTIONS An Overview

  2001cited by this paper
• The health status of obese individuals in Canada

  2001influential reference
• Consistent Moment Selection Procedures for Generalized Method of Moments Estimation

  1999influential reference
• Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments

  1998cited by this paper
• Clinical Guidelines on the Identification, Evaluation, and Treatment of Overweight and Obesity in Adults--The Evidence Report. National Institutes of Health.

  1998cited by this paper
• Identification of Causal effects Using Instrumental Variables

  1996influential reference
• Regression Shrinkage and Selection via the Lasso

  1996influential reference
• Two-Stage Least Squares Estimation of Average Causal Effects in Models with Variable Treatment Intensity

  1995cited by this paper
• Sparse Approximate Solutions to Linear Systems

  1995cited by this paper
• Estimation and inference in econometrics

  1994cited by this paper
• [On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9.] Comment: Neyman (1923) and Causal Inference in Experiments and Observational Studies

  1990cited by this paper
• Introductory Remarks on Neyman (1923)

  1990cited by this paper
• Causal Inference, Path Analysis and Recursive Structural Equations Models. Program Statistics Research, Technical Report No. 88-81.

  1988influential reference
• CAUSAL INFERENCE, PATH ANALYSIS AND RECURSIVE STRUCTURAL EQUATIONS MODELS

  1988cited by this paper
• The Estimation of Wage Gains and Welfare Gains in Self-selection

  1987cited by this paper
• Utility approach to measuring health-related quality of life.

  1987cited by this paper
• Estimation of Wage Gains and Welfare Gains from Self-Selection Models

  1983cited by this paper
• LARGE SAMPLE PROPERTIES OF GENERALIZED METHOD OF

  1982cited by this paper
• Estimating causal effects of treatments in randomized and nonrandomized studies.

  1974cited by this paper
• A Note on the Comparison of Ordinary and Two-Stage Least Squares Estimators

  1971cited by this paper
• Statistical Methods in Medical Research Mendelian Randomization as an Instrumental Variable Approach to Causal Inference Mendelian Randomization as an Instrumental Variable Approach to Causal Inference

  year unknowncited by this paper
• Large Sample Properties of Generalized Method of Moments Estimators

  year unknowncited by this paper

• Robust Weighted Triangulation of Causal Effects Under Model Uncertainty

  2026cites this paper
• Model-free feature screening for ultrahigh dimensional data with responses missing not at random

  2026cites this paper
• MACFIV: a novel framework for nonlinear causal inference in the body mass index–hypertension relationship with many weak and pleiotropic genetic instruments

  2026cites this paper
• Causal Effect Estimation with Learned Instrument Representations

  2026cites this paper
• HILAMA: High-dimensional multi-omics mediation analysis with latent confounding

  2025cites this paper
• Ice Cream Doesn't Cause Drowning: Benchmarking LLMs Against Statistical Pitfalls in Causal Inference

  2025cites this paper
• Enhancing Causal Effect Estimation with Diffusion-Generated Data

  2025cites this paper
• A latent outcome variable approach for Mendelian randomization using the stochastic expectation maximization algorithm

  2025cites this paper
• Bayesian Model Averaging in Causal Instrumental Variable Models

  2025influential citation
• MR-MAGIC: Robust Causal Inference Using Many Weak Genetic Interactions

  2025influential citation
• A Decision Theoretic Perspective on Artificial Superintelligence: Coping with Missing Data Problems in Prediction and Treatment Choice

  2025cites this paper
• Distributed Estimation and Inference for High-Dimensional Confounded Models

  2025cites this paper
• Debiased Continuous Updating GMM with Many Weak Instruments

  2025cites this paper
• Possibilistic Instrumental Variable Regression

  2025cites this paper
• Fiducial inference for partially identified parameters with applications to instrumental variable models

  2025cites this paper
• Leveraging specificity for causal inference in observational studies

  2025cites this paper
• A regression-based approach for bidirectional proximal causal inference in the presence of unmeasured confounding

  2025cites this paper
• How good are weather shocks for identifying energy elasticities? A LASSO-IV approach to European natural gas demand

  2025cites this paper
• Semiparametric Causal Discovery and Inference with Invalid Instruments

  2025cites this paper
• ti-scMR: trajectory-inference-based dynamic single-cell Mendelian randomization identifies causal genes underlying phenotypic differences

  2025cites this paper
• Partial causal identification for right censored data with noncompliance

  2025cites this paper
• Mendelian Randomization Methods for Causal Inference: Estimands, Identification and Inference

  2025cites this paper
• Innovation Diffusion Among Coworkers: Evidence from Senior Doctors

  2025cites this paper
• Testing the validity of instrumental variables in just-identified linear non-Gaussian models.

  2025cites this paper
• Identify key environmental factors and neglected genetic SNPs associated with obsessive-compulsive disorder by two-sample multivariate Mendelian randomization analysis.

  2025cites this paper
• Adaptive Proximal Causal Inference with Some Invalid Proxies

  2025influential citation
• Double Negative Control Inference With Some Invalid Negative Control Exposures for Continuous Outcome

  2025cites this paper
• Bounding Causal Effects with Leaky Instruments

  2024cites this paper
• Causal relationship between sex hormones and cutaneous melanoma: a two-sample Mendelian randomized study

  2024cites this paper
• Bayesian network-based Mendelian randomization for variant prioritization and phenotypic causal inference

  2024cites this paper
• Identification and Estimation of the Bi-Directional MR with Some Invalid Instruments

  2024cites this paper
• Nonparametric identification and efficient estimation of causal effects with instrumental variables

  2024influential citation
• Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Data

  2024cites this paper
• A Semi-parametric Estimation of Personalized Dose-response Function Using Instrumental Variables

  2024influential citation
• A focusing framework for testing bi-directional causal effects in Mendelian randomization.

  2024cites this paper
• Testing overidentifying restrictions on high-dimensional instruments and covariates

  2024cites this paper
• A Modified Debiased Inverse‐Variance Weighted Estimator in Two‐Sample Summary‐Data Mendelian Randomization

  2024cites this paper
• Identification and Inference with Invalid Instruments

  2024influential citation
• Discovery and inference of possibly bi-directional causal relationships with invalid instrumental variables

  2024cites this paper
• Penalized Semiparametric Estimation for Causal Inference with Possibly Invalid Instruments

  2024influential citation
• Hemorrhoidal disease and its genetic association with depression, bipolar disorder, anxiety disorders, and schizophrenia: a bidirectional mendelian randomization study

  2024cites this paper
• Genetic Causal Relationship Between Sex Hormones and Basal Cell Carcinoma: A Two-Sample Mendelian Randomization Study

  2024cites this paper
• Learning control variables and instruments for causal analysis in observational data

  2024cites this paper
• Automating the Selection of Proxy Variables of Unmeasured Confounders

  2024cites this paper
• Disentangled Representation Learning for Causal Inference With Instruments

  2024cites this paper
• Social-Science Genomics: Progress, Challenges, and Future Directions

  2024cites this paper
• Shifting the paradigm: Estimating heterogeneous treatment effects in the development of walkable cities design

  2024cites this paper
• Genetic causal relationship between gut microbiota and basal cell carcinoma: A two‐sample mendelian randomization study

  2024cites this paper
• LASSO-type instrumental variable selection methods with an application to Mendelian randomization

  2024influential citation
• Valid instrumental variable selection method using negative control outcomes and constructing efficient estimator

  2024cites this paper
• Distributed empirical likelihood inference with or without Byzantine failures

  2024cites this paper
• Inference of nonlinear causal effects with application to TWAS with GWAS summary data

  2024cites this paper
• Instrumental Variable Model Average With Applications in Nonlinear Causal Inference

  2024cites this paper
• Testability of Instrumental Variables in Additive Nonlinear, Non-Constant Effects Models

  2024cites this paper
• BudgetIV: Optimal Partial Identification of Causal Effects with Mostly Invalid Instruments

  2024cites this paper
• Best-subset instrumental variable selection method using mixed integer optimization with applications to health-related quality of life and education–wage analyses

  2024influential citation
• RobustIV and controlfunctionIV: Causal Inference for Linear and Nonlinear Models with Invalid Instrumental Variables

  2023cites this paper
• Unbiased estimation and asymptotically valid inference in multivariable Mendelian randomization with many weak instrumental variables

  2023influential citation
• MRBEE: A novel bias-corrected multivariable Mendelian Randomization method

  2023cites this paper
• simmrd: An open-source tool to perform simulations in Mendelian randomization

  2023cites this paper
• Causal Discovery with Generalized Linear Models through Peeling Algorithms

  2023cites this paper
• HILAMA: High-dimensional multi-omic mediation analysis with latent confounding

  2023cites this paper
• Identifying Causal Effects Using Instrumental Variables from the Auxiliary Population

  2023cites this paper
• Discovery and Inference of a Causal Network with Hidden Confounding

  2023influential citation
• The Value of Virtual Engagement: Evidence from a Running Platform

  2023cites this paper
• Inference of causal metabolite networks in the presence of invalid instrumental variables with GWAS summary data

  2023cites this paper
• Nonlinear Estimation Methods for Mendelian Randomization in Genetic Studies

  2023cites this paper
• Robust Inference for Federated Meta-Learning

  2023cites this paper
• A Bayesian approach to Mendelian randomization using summary statistics in the univariable and multivariable settings with correlated pleiotropy

  2023cites this paper
• Identifiability of causal effects with non-Gaussianity and auxiliary covariates

  2023cites this paper
• Nonparametric instrument model averaging

  2023cites this paper
• Instrumental variable model average with applications in Mendelian randomization

  2023cites this paper
• Identification and Estimation of Causal Effects Using non-Gaussianity and Auxiliary Covariates

  2023cites this paper
• A bidirectional Mendelian randomized study of classical blood lipids and venous thrombosis

  2023cites this paper
• Causal Inference with Secondary Outcomes

  2023cites this paper
• Selecting Valid Genetic Instruments and Constructing Robust Confidence Intervals for Two-sample Mendelian Randomization Using Genome-wide Summary Statistics

  2023influential citation
• Summarising multiple bounds of the average causal effect in Mendelian randomisation.

  2023cites this paper
• Causal Inference in Transcriptome-Wide Association Studies with Invalid Instruments and GWAS Summary Data

  2023cites this paper
• Personalized Pricing with Invalid Instrumental Variables: Identification, Estimation, and Policy Learning

  2023cites this paper
• Sequential Underspecified Instrument Selection for Cause-Effect Estimation

  2023cites this paper
• MR‐BOIL: Causal inference in one‐sample Mendelian randomization for binary outcome with integrated likelihood method

  2023cites this paper
• Mendelian randomization with incomplete measurements on the exposure in the Hispanic Community Health Study/Study of Latinos

  2023cites this paper
• The synthetic instrument: From sparse association to sparse causation

  2023cites this paper
• Unbiased metabolome screen leads to personalized medicine strategy for amyotrophic lateral sclerosis

  2022cites this paper
• A Focusing Framework for Testing Bi-Directional Causal Effects with GWAS Summary Data

  2022cites this paper
• Fighting Noise with Noise: Causal Inference with Many Candidate Instruments

  2022cites this paper
• Mendelian randomization

  2022cites this paper
• The Falsification Adaptive Set in Linear Models with Instrumental Variables that Violate the Exogeneity or Exclusion Restriction

  2022cites this paper
• Instrumental Variables in Causal Inference and Machine Learning: A Survey

  2022cites this paper
• Identification of causal effects of neuroanatomy on cognitive decline requires modeling unobserved confounders

  2022cites this paper
• Causal Inference with Conditional Instruments using Deep Generative Models

  2022cites this paper
• Ancestral instrument method for causal inference without a causal graph

  2022cites this paper
• Distributed lags using elastic-net regularization for market response models: focus on predictive and explanatory capacity

  2022cites this paper
• Considering strategies for SNP selection in genetic and polygenic risk scores

  2022cites this paper
• Assessing the Most Vulnerable Subgroup to Type II Diabetes Associated with Statin Usage: Evidence from Electronic Health Record Data

  2022cites this paper
• Data-driven Automated Negative Control Estimation (DANCE): Search for, Validation of, and Causal Inference with Negative Controls

  2022cites this paper
• Inference of nonlinear causal effects with GWAS summary data

  2022cites this paper
• Identifiability of sparse causal effects using instrumental variables

  2022cites this paper
• Almost exact Mendelian randomization

  2022cites this paper
• High-Dimensional Inference for Generalized Linear Models with Hidden Confounding

  2022cites this paper